| 简介： | Abstract:
To capture the conditional heteroskedasticity of non-Gaussian time series, this paper extends the class of generalized autoregressive moving average (GARMA) models to the GARCH type of GARMA models, called the GARMA-GARCH models. Based on Zheng, Xiao, and Chen’s (2014) M-GARMA framework, the error sequence being a martingale difference sequence is further assumed to follow a semi-strong GARCH process. Under this semi-strong GARCH case, the solution of second-order stationarity is derived. We propose three specific models for proportional time series, nonnegative time seris, and skewed and heavy-tailed financial time series, respectively. Two estimation methods including maximum likelihood estimator (MLE) and Gauss pseudo MLE (GMLE) are then introduced for estimating the parameters. Simulation results with two examples show that the GMLE performs well and the associated parameter estimates can be used as good starting values of the MLE. Finally, three empirical investigations are carried out on realized volatility, U.S. personal saving rates and daily returns, respectively. |